Volume 78, Number 6, June 2007
|Number of page(s)||6|
|Published online||22 May 2007|
Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.) Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
Accepted: 27 April 2007
We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.
PACS: 03.65.Vf – Phases: geometric; dynamic or topological / 03.75.Ss – Degenerate Fermi gases / 05.60.Gg – Quantum transport
© Europhysics Letters Association, 2007
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